Think about it this way: if you could do it with a random computer on the network without special cooperation from the router, what would stop someone from connecting to your network with this software you propose and doing the same? As I explained, telling your router to instruct your clients to use a particular DNS server isn't nearly enough.
The closest you could get would be to use another computer with 2 network cards as the actual router (running something like PFSense), and set up a consumer WiFi router as an access point instead of a router. This would only work as long as you don't mind the clients being able to connect to the rest of you local network; if that's an issue you really need something like a captive portal aware AP/switch or a VLAN.
However this solution doesn't make much sense in the end, as it would be much cheaper to buy one of the cheaper commercial-grade APs (UniFi's are around $80) and use your "regular router" with WiFi disabled than it is to buy a computer for that purpose. Those APs are also better quality than any consumer router you could find, and scale up much better for larger venues.
Also TBH if you're not aware of how captive portals work and why it can't be done by a random computer on your network, this is probably not a good business venture for you. This isn't an unsolved (or expensive to solve) problem to begin with.